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Small as it appears, how big would that planet have to be to register as an image of (?) pixels from 1200 light years away?

Good question. In professional telescopes and other professional optics pixel pitch (pixels per millimeter) are matched to optical resolution. The resolving power of an optical system is in radians is:

ds = 1.22 x wavelength / aperture

where:

ds = resolving power in radians
1.22 = empirical constant for a circular aperture
wavelength = optical wavelenth, use 550 nanometers for visible light
aperture = objective diameter in the same units as wavelength.

For the Hubble Space telescope that works out to about 2.29 x 10^-7 radians. The resolution at 1200 light years would be about 2.6 billion kilometers or 17 AU. For two objects to be resolvable to the HST at that distance they would have to about 17 times the distance between the earth and sun apart.

At the distance to Pluto (40 AU) the resolution of the HST is about 1375 km about half the diameter of Pluto, 2377 km. Pluto would occupy four pixels, two horizontally, two vertically, in the HST.

Hmmm...this is very curious, indeed.

At this point, I’m struggling with the implications that, at 1200 light years, one pixel in the image = 17 AU (if taken by the HST). The “tiny tiny brown dot” in the article image is what? ... two pixels wide and two pixels high?

Stars can, of course, be of enormous sizes.

(https://en.wikipedia.org/wiki/List_of_largest_stars)

It’s unfathomable to think of a planet 34 AU in diameter. Is that even possible geologically?

Yet the only variable at play in the equation you provided is the size of the aperture (diameter) . Hubble’s is 2.4 meters. How much larger are the mirrors on the telescopes at the participating observatories? How much larger would they have to be to get the planet down to say, ... Jupiter size or even 1 AU?

On the other hand, this “planet” began as a pixilated image that subsequently has been reproduced digitally and manipulated digitally (perhaps many times). The image size could be an observational approximation being provided by the processing algorithms; a mathematical way of saying “I saw something here.” Or it could be some text editor’s attempt to assist the general reader.

Either way (or perhaps some other way), its true size and composition is for some very distant future generation to know. File it away in the box marked “Unanswerable Questions.”

Thanks for entertaining my comments and questions and providing informative answers.

Be well.